1. Field of the Invention
The present invention concerns: a method to calculate individual elements of a matrix to correct artifacts in magnetic resonance images that are created by means of an MR pulse sequence in which gradients are activated simultaneously during the radiation of at least one excitation pulse, as well as a magnetic resonance system and an electronically readable data medium for implementing such a method.
2. Description of the Prior Art
Magnetic resonance (MR) (also known as magnetic resonance tomography), is a known modality with which images of the inside of an examination subject can be generated. Expressed in a simplified form, the examination subject is positioned in a strong, static, homogeneous basic magnetic field (also called a B0 field) with a field strength from 0.2 Tesla to 7 Tesla or more in a magnetic resonance apparatus, such that the nuclear spins of the examination subject orient along the basic magnetic field. To trigger magnetic resonance signals, radio-frequency excitation pulses (RF pulses) are radiated into the examination subject, and the triggered magnetic resonance signals are measured as k-space data, on the basis of which MR images are reconstructed or spectroscopy data are determined. For spatial coding of the measurement data, rapidly switched magnetic gradient fields are superimposed on the basic magnetic field. The acquired measurement data are digitized and stored as complex numerical values in a k-space matrix. An associated MR image can be reconstructed from the k-space matrix populated with values, such as by means of a multidimensional Fourier transformation.
Sequences with very short echo times TE—for instance TE less than 0.5 milliseconds—offer new fields of application for magnetic resonance tomography. They enable the depiction of substances that cannot be depicted with conventional sequences such as (T)SE ((Turbo) Spin Echo) or GRE (gradient echo) since their respective decay time of the transversal magnetization M2 is markedly shorter than the possible echo times of the conventional sequences, and their signal has therefore already decayed at the point in time of acquisition. In contrast, with echo times in the range of these decay times it is possible to depict the signals of these substances in an MR image, for example. The decay times T2 of teeth, bones or ice lie between 30 and 80 microseconds, for example.
The application of sequences with ultrashort echo times (UEZ sequences) thus enables (for example) bone and/or dental imaging and/or the depiction of cryoablations by means of MR, and is usable for MR-PET (combination of MR and positron emission tomography, PET) or PET attenuation correction.
Examples of UEZ sequences are: UTE (“Ultrashort Echo Time”), for example as described in the article by Sonia Nielles-Vallespin, “3D radial projection technique with ultrashort echo times for sodium MRI: Clinical applications in human brain and skeletal muscle”, Magn. Res. Med. 2007, 57, Pages 74-81; PETRA (“Pointwise Encoding Time reduction with Radial Acquisition”) as described by Grodzki et al. in “Ultra short Echo Time Imaging using Pointwise Encoding Time reduction with Radial Acquisition (PETRA)”, Proc. Intl. Soc. Mag. Reson. Med. 19 (2011), Page 2815; or z-TE as described by Weiger et al. in “MRI with zero echo time: hard versus sweep pulse excitation”, Magn. Reson. Med. 66 (2011), Pages 379-389.
In these sequences, usually a hard delta pulse is applied as a radio-frequency excitation pulse and the data acquisition is subsequently begun. In PETRA or z-TE, the gradients are already activated during the excitation. The spectral profile of the excitation pulse hereby corresponds approximately to a sin c function. If the pulse bandwidth is insufficient or the gradients are too strong, the outer image regions are no longer sufficiently excited. In the reconstructed MR image, this incorrect excitation has the effect of causing blurring artifacts at the image edge, which are more strongly pronounced the stronger the gradients that are switched during the excitation.
An insufficient excitation thus leads to artifact-plagued MR images. This problem has previously for the most part been negligible. At most, it is sought to optimally reduce the strength of the gradients. However, imaging-relevant variables (such as the readout bandwidth, the repetition time TR and the contrast of the image) are changed as a result of this gradient field strength reduction. For example, a reduction of the gradient strength increases the minimum necessary repetition time TR, and therefore also the total measurement time. Such artifacts could furthermore be reduced by choosing the excitation pulses to be particularly short, in order to increase the excitation width. However, the maximum possible flip angle and the precision of the actual emitted RF excitation pulse are simultaneously reduced in proportion to the duration of the RF excitation pulse. For example, for a duration of the excitation pulse of 14 microseconds, the maximum flip angle is approximately 9°, and for a reduced duration of the excitation pulse to 7 microseconds, the maximum flip angle would be only approximately 4.5°. Therefore, this procedure is also not usable without limitation and incurs a degradation of the image quality.